I think they should absolutely be different. The USS Enterprise is a good example. There have already been 8 US Naval vessels to bear that name, with a 9th in the planning stages. AND that doesn't count the USS Enterprise from Star Trek.
In addiion to commission years or something like that, another possible differentiator is the alphanumeric designation:
USS Enterprise: aircraft carrier from 1936 to 1946: CV-6 ("Carrier Vessel-6")
USS Enterprise: nuclear aircraft carrier from 1961 to 2012: CVN-65 ("Carrier Vessel, Nuclear-65")
USS Enterprise: nuclear carrier in production: CVN-80
USS Enterprise: starship from Star Trek: NCC-1701